Abstract
Vibration analysis of linear plates has been carried out in Chapter 2 on the basis of the exact elasticity theory. In this chapter, we again start from the elasticity theory, but proceed now to first derive linear equations of plates, which are then applied to the vibration analysis. As already mentioned, the plate equations are always approximate in nature from the standpoint of elasticity theory, but they are also always simpler to apply than the original elasticity equations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Kane, T.R. and R.D. Mindlin (1956) High-Frequency Extensional Vibrations of Plates. Journal of Applied Mechanics, Vol. 23, pp. 277–283.
Mindlin, R.D. (1951a) Influence of Rotatory Inertia and Shear on Flexural Motions of Isotropic, Elastic Plates. Journal ofApplied Mechanics, Vol. 18, pp. 31–38.
Mindlin, R.D. (1951b) Thickness-Shear and Flexural Vibrations of Crystal Plates. Journal of Applied Physics, Vol. 22, pp. 316–323.
Mindlin, R.D. (1961) High Frequency Vibrations of Crystal Plates. Quarterly of Applied Mathematics, Vol. 19, pp. 51–61.
Mindlin, R.D., A. Schacknow, and H. Deresiewicz (1956) Flexural Vibrations of Rectangular Plates. Journal of Applied Mechanics, Vol. 23, pp. 430–436.
Mindlin, R.D. and M.A. Medick (1959) Extensional Vibrations of Elastic Plates. Journal of Applied Mechanics, Vol. 26, pp. 561–569.
Reissner, E. (1945) The Effect of Transverse Shear Deformation on the Bending of Elastic Plates. Journal of Applied Mechanics, Vol. 67, pp. A-69–A-77.
Timoshenko, S. (1921) On the Correction for Shear of the Differential Equation for Transverse Vibrations of Prismatic Bars. Philasophical Magazine, Vol. 41, pp. 744–746.
Timoshenko, S. and S. Woinowsky-Krieger (1959). Theory of Plates and Shells, 2nd Ed. McGraw-Hill, New York.
Yu, Y.Y. (1965) On Linear Equations of Anisotropic Elastic Plates. Quarterly of Applied Mathematics, Vol. 22, pp. 357–360.
Yu, Y.Y. (1992) Equations for Large Deflections of Elastic and Piezoelectric Plates and Shallow Shells, Including Sandwiches and Laminated Composites, with Applications to Vibrations, Chaos, and Acoustic Radiation. Presented at the XIIIth International Congress of Theoretical and Applied Mechanics, Haifa, Israel.
Yu, Y.Y. (1995) On the Ordinary, Generalized, and Pseudo-Variational Equations of Motion in Nonlinear Elasticity, Piezoelectricity, and Classical Plate Theories. Journal of Applied Mechanics, Vol. 62, pp. 471–478.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Yu, YY. (1996). Linear Modeling of Homogeneous Plates. In: Vibrations of Elastic Plates. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2338-2_3
Download citation
DOI: https://doi.org/10.1007/978-1-4612-2338-2_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7509-1
Online ISBN: 978-1-4612-2338-2
eBook Packages: Springer Book Archive